Finite element simulation of flexible roll forming with supplemented material data and the experimental verification

Flexible roll forming is a promising manufacturing method for the production of variable cross section products. Considering the large plastic strain in this forming process which is much larger than that of uniform deformation phase of uniaxial tensile test, the widely adopted method of simulating the forming processes with non-supplemented material data from uniaxial tensile test will certainly lead to large error. To reduce this error, the material data is supplemented based on three constitutive models. Then a finite element model of a six passes flexible roll forming process is established based on the supplemented material data and the original material data from the uniaxial tensile test. The flexible roll forming experiment of a B pillar reinforcing plate is carried out to verify the proposed method. Final cross section shapes of the experimental and the simulated results are compared. It is shown that the simulation calculated with supplemented material data based on Swift model agrees well with the experimental results, while the simulation based on original material data could not predict the actual deformation accurately. The results indicate that this material supplement method is reliable and indispensible, and the simulation model can well reflect the real metal forming process. Detailed analysis of the distribution and history of plastic strain at different positions are performed. A new material data supplement method is proposed to tackle the problem which is ignored in other roll forming simulations, and thus the forming process simulation accuracy can be greatly improved.     

Fracture analysis on flexible roll forming process of anisotropic Al6061 using ductile fracture criteria and FLD

In this research, the fracture phenomenon was investigated on flexible roll forming process of channel section using ductile fracture criteria and forming limit diagram (FLD) by considering the effect of anisotropy. For this purpose, a finite element simulation of the process using the ABAQUS software was done. The fracture in this process was evaluated by considering six types of ductile fracture criteria by UMAT subroutine implementation on the FEM software and using FLD criterion. Experimental tests were performed on 27 blanks of Al6061-T6 using flexible roll forming machine made in Shahid Rajaee Teacher Training University (SRTTU). Numerical results were validated by experimental results. In addition, prediction of occurrence and fracture position by ductile fracture criteria and FLD criterion were compared with experimental results; the Argon criterion was chosen as the most appropriate criterion to predict the fracture position and its occurrence. The fracture occurrence was only observed in a 60° bending angle for 1.5- and 2-mm thicknesses, and the fracture position error percentages of the Argon criterion with experiments for these cases were 18.7 and 3.5%, respectively. Also, the effects of parameters such as sheet thickness, bending radius, and bending angle on the fracture phenomenon by using the selected criterion of Argon were studied.     

Extension of the Hill (1948) yield criterion to the case of prismatic monoclinic symmetry

The theory of the invariant representation for tensor functions in first illustrated by providing a general form of the Hill (1948) orthotropic yield criterion. It is then applied to derive a quadratic yield equation for the case of prismatic monoclinic symmetry, which is induced by simple shear deformation. This new criterion can in turn be approximated by an orthotropic one by choosing the ‘best’ symmetry axes. The above equations are then used to derive the angular dependences of the uniaxial yield stress and strain rate ratio in the plane of a prismatic monoclinic sheet. Finally, it is shown on an example that they are able to predict the axial stresses occurring during torsion testing with a fairly good accuracy.     

参数求解方法对屈服准则的各向异性行为描述能力的影响

详细分析基于应力各向异性和变形各向异性两种求解Hill48屈服准则参数的方法。在给出两种各向异性参数求解表达式的基础上,具体分析Hill48屈服准则本身的局限性。以5754O铝合金板为研究对象,进行不同方向的单向拉伸试验。采用两种各向异性参数求解方法,基于Hill48屈服准则推导不同方向拉伸过程中的理论应力-应变曲线和拉伸过程中的变形规律。通过对比理论与试验结果具体分析参数求解方法对屈服准则精度的影响。基于两种参数求解方法,进行5754O铝合金板拉深试验的有限元模拟,讨论不同求解方法对凸耳现象的描述精度。得出结论：当对应力各向异性为主的问题进行分析时,应采用应力各向异性法求解;当对变形各向异性为主的问题进行分析时,则应采用变形各向异性法求解。研究结果对屈服准则在板料成形方面的合理应用具有重要的参考价值。     

Modeling and simulation for multiple-step incremental air-bending forming of sheet metal

Based on Hill’s yielding criterion and plane strain condition, the explicit expressions of elastoplastic constitutive model are derived in this paper which takes into account the effects of transverse stress, neutral surface shifting, and sheet thickness thinning on the sheet springback of air-bending. Then, this model is embedded into ABAQUS software platform by means of programming. Finally, 3D ABAQUS finite-element models (FEM), used to form the semiellipse-shaped workpiece with super length and large opening of sheet metal, are established, and the multiple-step incremental air-bending forming and springback processes are simulated. The simulation and experiment results show that the data predicted with the new constructed constitutive model under the plane strain condition are in much better agreement with experimental data than those predicted with the constitutive model built-in ABAQUS. It can be taken as a valuable mathematical tool used for multiple-step incremental air-bending forming simulation of large area sheet metal.     

Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet

Forming limit curves at neck and at fracture have been experimentally determined, and surfaces of fractured dome specimens have been observed optically and in the SEM, for an automotive AA6111-T4 sheet material. Various continuum ductile fracture criteria from the literature along with the assumptions of power law hardening, Hill’s quadratic yield criterion, and proportionality of stress and strain paths have been utilized for prediction of forming limit curve at fracture and compared with the experimental curve to assess the applicability of the different fracture criteria. The maximum shear stress criterion by Tresca predicts reasonably well the fracture limits of AA6111-T4 sheet material for a range of strain ratios, and is consistent with the microstructural observations. The criterion can be used to predict fracture limit curves from uniaxial tensile data and plane strain limit at fracture. A methodology for incorporating such a ductile fracture criterion into FE simulations of sheet stampings for prediction of fracture is discussed.     

Wrinkling criterion for an anisotropic shell with compound curvatures in sheet forming

Wrinkling criteria are proposed for an elastic isotropic and plastic anisotropic shell with compound curvatures in the noncontact region of a sheet subjected to internal forming stresses. A quasi-shallow shell is modeled by Donnell-Mushtari-Vlasov (DMV) shell theory. A bifurcation functional from Hill's general theory of uniqueness and bifurcation in elastic-plastic solids is used to model the local wrinkling phenomenon. Both strain hardening and transverse anisotropy are taken into consideration. This wrinkling criterion is especially useful as a failure criterion in three dimensional finite element modeling (FEM) of sheet forming. Given the principal stresses or strains and the geometry provided at each incremental deformation step, the criterion can be used to predict wrinkles in the elements in the unsupported region.     

Analytical modeling and numerical simulation for three-roll bending forming of sheet metal

The three-roll bending forming of sheet metal is an important and flexible manufacturing process due to simple configuration. It is suitable for forming large sheet parts with complex, curved faces. Most researches on roll bending forming of large workpiece are mainly based on experiments and explain the process through macroscopic metal deformation. An analytical model and ABAQUS finite element model (FEM) are proposed in this paper for investigating the three-roll bending forming process. A reasonably accurate relationship between the downward inner roller displacement and the desired springback radius (unloaded curvature radius) of the bent plate is yielded by both analytical and finite element approaches, which all agree well with experiments. Then, the three-roll bending forming process of a semi-circle-shaped workpiece with 3,105 mm (length)?×?714 mm (width)?×?545 mm (height) is simulated with FEM established by the optimum tool and process parameters. Manifested by the experiment for three-roll bending forming of this workpiece, the numerical simulation method proposed yields satisfactory performance in tool and process parameters optimization and workpiece forming. It can be taken as a valuable mathematical tool used for three-roll bending forming of large area sheet metal.     

高强钢板DP590温热环境下屈服准则适用性分析

板料成形过程中温度的变化会影响其塑性流动行为。以先进高强钢板DP590为研究对象,通过不同温度下单拉试验和不同温度不同加载比例双拉试验得到其在温热环境下的试验屈服轨迹,结果显示温度不仅会影响DP590钢板屈服轨迹的大小,而且影响屈服轨迹的形状。将试验屈服轨迹和几种理论屈服轨迹进行对比分析,表明Yld2000-2D屈服准则与试验结果吻合较好,同时等效应力应变点分析也显示出Yld2000-2D屈服准则满足塑性力学的单一曲线假设规律。针对Yld2000-2D屈服准则,采用不同温度下的试验数据计算出不同温度下的各向异性参数,通过拟合获得各向异性参数与温度的四次多项式函数关系,建立温度相关Yld2000-2D屈服准则,并与常规Yld2000-2D屈服准则对比分析,结果显示温度相关Yld2000-2D屈服准则更加适合描述DP590钢板温热环境下的屈服行为。     

Optimized bending angle distribution function of contour plate roll forming

Regarding the roll forming of contour plates, traditional roll forming techniques often result in peak longitudinal strain during the forming process, which causes defects such as longitudinal bowing and springback. The bending angle, sheet thickness, and the number of forming passes are all important process parameters that cause the aforementioned problems. This study proposes quantifying the projection track regarding the edge of the profile section in the horizontal plane that follows a cubic curve and uses the curve function to reasonably distribute the bending angle to study the maximum forming strain and the average strain for all passes of the sheet between the forming passes. Simultaneously, the influence law of the sheet thickness and number of forming passes was studied. Based on theoretical simulation and experimental verification, the optimal bending angle distribution function is A1: y?=?x³?+?x²?+?x. When the thickness of the sheet is 1.5 mm, both the maximum forming strain between the passes during roll forming and the average strain of all passes are the smallest, which are 3.91 and 0.609%, respectively. Moreover, with the increase in the number of passes, the longitudinal bowing and springback decrease to varying degrees.     

柔性冷弯成型实验研究

柔性冷弯成型是板金属成形技术的前沿研究领域之一。柔性冷弯成型技术研究中,研制了柔性双轴变截面冷弯成型机;以柔性双轴变截面冷弯成型机为平台进行了柔性冷弯成型实验研究,成型出了变截面U型样件,并对样件出现成型缺陷的原因进行了分析,为进一步的深入研究奠定了基础。     

基于厚度梯度准则的薄板成形极限图建立方法

介绍一种预测薄板成形极限的新准则——厚度梯度准则,该准则基于薄板颈缩时沿垂直于颈缩方向的厚度梯度分布存在极值RC。在薄板成形过程中,当板面内的厚度梯度值小于临界厚度梯度值RC时,认为薄板发生颈缩。基于厚度梯度准则,结合对IF钢成形极限试验的有限元仿真,计算获得其成形极限图,计算结果与试验数据吻合较好。将厚度梯度准则与有限元方法相结合,可在已知薄板单拉性能参数的条件下计算获得其成形极限图。     

Sectional finite element analysis of forming processes for aluminum-alloy sheet metals

The sectional finite element analysis of the forming processes for the aluminum-alloy sheet metal known to be planar anisotropic was performed. The two-dimensional rigid-viscoplastic FEM formulation based on the bending augmented membrane theory as well as the anisotropic yield criteria was introduced. For modeling the anomalous behavior of aluminum-alloy sheet metals, Barlat's strain rate potential and Hill's (Journal of the Mechanics and Physics of Solids 1990;38:405–17) non-quadratic yield theory with an isotropic hardening rule were employed. Furthermore, a new method to determine anisotropic coefficients of Barlat's strain rate potential was proposed. For evaluating bending effects in the forming process of aluminum-alloy sheet metals, the bending equivalent forces were calculated in terms of the changes in the interior angle at a node between two linear finite elements and were augmented to the membrane stretch forces. In order to verify the validity of sectional finite element formulation based on the bending augmented membrane theory, the plane strain stretch/draw forming processes of a square cup test were simulated and simulation results are compared with experimental measurements. Friction coefficient was obtained from drawbead friction test. The properties of selected material were obtained from uniaxial tensile tests. Simulation shows good agreement with measurements. For the application of the sectional finite element formulation introduced in this research, the drawing process of a rear seat back upper bracket of passenger cars is simulated assuming plane strain condition. The thinning distribution of the simulation agreed well with that of the measurement, so that the sectional analysis is acceptable in the design and analysis of aluminum-alloy sheet stamping dies.     

基于成形应力极限的管材液压成形缺陷预测

基于塑性应力应变关系及Hill79屈服准则,推导出极限应力与极限应变间转化关系,进而建立2008T4铝合金的成形应力极限图(Forming limit stress diagram,FLSD)。采用LS-DYNA软件对三通管液压胀形过程进行模拟,应用FLSD预测胀形过程中破裂的发生及成形压力极限,并与传统成形极限图(Forming limit diagram,FLD)结果进行了对比。研究表明,FLD与FLSD预测结果中破裂缺陷位置相同,但极限内压力值存在很大差别,而FLSD预测结果与物理试验结果较吻合。考虑到FLD受应变路径影响显著的因素,将FLSD作为管材液压成形等复杂应变路径下的成形极限的判据更加方便可靠。     

Characterization and modeling of the mechanical behavior and formability of a 2008-T4 sheet sample

A 2008-T4 sheet sample has been characterized and its mechanical behavior and formability have been modeled. Uniaxial tensile and equal biaxial tensile stress-strain data, compressive yield strengths, crystallographic texture, earing and the forming limit curve were experimentally determined. Bulge test specimen shape and thickness profiles were also measured after various amounts of biaxial strain. A recently developed phenomenological constitutive model of anisotropic mechanical behavior was used to predict the directionality of strength, plastic strain ratio (R) and shear strain ratio (Г) values. In addition, this model was used to predict the forming limit curve for this sample. Predictions made with the recent model generally compare favorably with experimental results and with predictions made using the Taylor/Bishop and Hill theory. According to the data obtained in hydraulic bulge testing, the 2008-T4 exhibited apparent isotropic behavior. However, in cup drawing—another axisymmetric deformation mode—this material exhibited anisotropic behavior, as indicated by the formation of ears and troughs.     

阵列微流道电场辅助辊压成形技术研究

提出了电场辅助辊压成形制备大面积阵列微流道结构的工艺方法,修正了传统辊压理论模型,发现增大辊半径和辊齿间隙与齿宽之比可以提高填充高度。通过建立阵列微流道电流辅助热-电-力耦合有限元仿真模型确定了“板对板”通电方式以及辊压工艺方案,开展了不同工艺参数下电场辅助SUS304不锈钢阵列微流道辊压成形试验。结果表明,在辊压成形过程中,板材表面温度分布均匀,但板材横截面电流密度分布不一致,导致微流道不同区域应力分布不同,高密度电流可以降低流动应力的大小且减弱微流道不同区域应力的差异。在工艺参数方面,适当增大辊压力可以提高微流道成形质量,较低的同步辊速有利于微流道的成形。在最佳工艺参数组合下制造出的微流道平均宽度为0.302 mm±0.011 mm,平均深度为0.362 mm±0.010 mm。     

Modeling the material behavior of magnesium alloy AZ31 using different yield criteria

Nowadays, the finite element analysis (FEA) is playing a main rule in fields of sheet metal forming for designing processes and dimensioning parts. The most frequent yield criteria used in the FE commercial programs for the sheet-metal-forming simulation, like AUTOFORM, PAMSTAMP, etc., are Hill’48 for common steels or Barlat’89 and various BBC models for some aluminum alloys. In this paper, different yield loci for biaxial tensile stress conditions of the magnesium sheet metal alloy AZ31 are investigated. The experimental investigations have been done using the specimen geometry for the experimental setup developed at the Chair of Manufacturing Technology (LFT) of the University of Erlangen. The yielding behavior is determined basing exclusively on real material data out of experiments so that no FE calculations are necessary to detect strains and stresses. Using these data, several yield criteria are applied to approximate the real material characteristics, whereas the model of BBC’2005 leads to the best agreement for uniaxial yield stresses, the anisotropy coefficients, and the yield locus.     

Approximate yield criterion for voided anisotropic ductile materials

As most fractures of ductile materials in metal forming processes occurred due to the results of evolution of internal damage — void nucleation, growth and coalescence. In this paper, an approximate yield criterion for voided (porous) anisotropic ductile materials is developed. The proposed approximate yield function is based on Gurson’s yield function in conjunction with the Hosford’s non-quadratic anisotropic yield criterion in order to consider the characteristic of anisotropic properties of matrix material. The associated flow rules are presented and the laws governing void growth with strain are derived. Using the proposed model void growth of an anisotropic sheet under biaxial tensile loading and its effect on sheet metal formability are investigated. The yield surface of voided anisotropic sheet and void growth with strain are predicted and compared with the experimental results.     

Prediction of forming limits for anisotropic sheets containing prolate ellipsoidal voids

In sheet metal forming operations, the formability of sheet metals is limited by the occurrence of internal damage evolution that eventually yields a localized neck. Thus, designing and optimizing a sheet metal forming process, requires the precise prediction of the forming limits of the sheet materials. Accordingly, the current work attempts to theoretically predict the forming limit diagrams (FLDs) of voided anisotropic sheets using a new version of the Marciniak and Kuczynski (M–K) model. The analysis employs Gologanu–Leblond–Devaux's yield function for materials containing axisymmetric prolate ellipsoidal cavities with random orientations in conjunction with Barlat and Lian's 1989 anisotropic yield criterion. The effect of a void shape parameter on a ductile material under biaxial tensile loading is introduced and examined within the framework of the M–K model, along with the effect of including a first-order strain gradient term in the flow stress. To confirm the validity of the proposed M–K model, the predicted FLDs were compared with experimental results for steel sheets. The predicted forming limits for the voided sheets were found to agree well with the experimental data.     

复合变形路径下的板材冲压成形极限应变(Ⅰ)——冲压成形极限应变的立论与解析

从4个方面就变形路径对成形极限图影响的研究现状进行综述,并进一步论述了复杂变形路径和单一变形路径的概念,以及基于Hill'48屈服准则的塑性应变几何关系.为了在任意复杂变形路径下计算冲压板材的失稳极限应变,提出"任意复杂变形路径均可简化为线性复合变形路径"、"板材的冲压成形能力亦即板材允许的极限厚度应变",以及"板材在线性复合变形路径下的冲压成形能力取决于其最终变形路径的应变比值"等3个工程简化假设,并对它们进行立论和诠释.同时基于这些假设,在板材承受线性复合变形路径和前后变形路径的应变主轴发生转动的条件下,解析和推导出计算冲压成形极限应变的理论公式.利用这些简化假设和理论公式,可以在任意复杂变形路径下计算板材的冲压成形极限应变并绘制其冲压成形极限图.